I am new to this forum. I need to solve a problem by optimizing it. I would like to know if there is a way to linearize or to obtain a quadratic function from the following objective function.
min $\beta + \frac{\gamma}{x} + x\delta $
s.t. $x \geq 1$
$x \in N$
The only decision variable is $x$. The original idea that I had was to multiply everything for $x$. That would lead to the following equation
min $x\beta + \gamma + x^2\delta $
which does not have the same derivative of the previous one and therefore it does not lead to the same solution. Or maybe I did something wrong in the process? Can anybody help me with this?